WASHINGTON -- The two congressional committees investigating General Motors’ recall crisis said today that they will hold follow-up hearings, with GM CEO Mary Barra and independent investigator Anton Valukas invited to testify.

The two committees are the House Energy and Commerce Committee and the Senate Commerce Committee, which grilled Barra at back-to-back hearings on April 1 and 2. Barra frustrated lawmakers during those hearings by deferring to Valukas’ investigation, responding to dozens of questions by saying she couldn’t comment until his report was complete.

Now they’ll get another shot at some answers.

“I have said that I will come back,” Barra told reporters this morning.

Energy and Commerce Chairman Fred Upton, R-Mich., said in a statement that he spoke with Barra this morning. He said she promised to testify at a hearing that will be held “in the coming weeks.” Valukas also is expected to attend.

“It will take time to scrutinize this over-300-page report, but the initial findings are deeply disturbing, suggesting that communications and management failures ran deep and wide within GM,” Upton said. “It has been more than a decade since we put tough new standards in place so automakers and regulators could quickly spot patterns and fix safety risks,” he added, “yet this devastating design flaw slipped through the cracks. It's unacceptable.”

To date, Upton’s committee has received 1 million pages of documents from GM and 15,000 pages of documents from the National Highway Traffic Safety Administration. It also has interviewed past and present GM executives, including the now-fired engineer Ray DeGiorgio, who was responsible for the ignition switch design.

U.S. Sen. Claire McCaskill, D-Mo., said the Senate Commerce subcommittee on consumer protection, of which she is chairman, plans a follow-up hearing for “later this summer.” She, too, wants Valukas to testify.

“I’m going to reserve judgment until I can take a closer look at the report -- which I expect to find comprehensive and thorough -- and I’m looking forward to getting a full briefing from Mr. Valukas,” McCaskill said in a statement. “I won’t be letting GM leadership, or federal regulators, escape accountability for these tragedies.”

Lawmakers have put forward several bills in response to the GM crisis.

One legislative proposal, from Sens. Edward Markey, D-Mass., and Richard Blumenthal, D-Conn., would allow members of the public to view the early-warning reports that automakers submit to NHTSA when they find a potential safety concern.

Another bill from Blumenthal and Sen. Lindsey Graham, R-S.C., called the Sunshine in Litigation Act, would stop companies from reaching confidential product liability settlements with customers when the public interest would be served by making information on that defect public. Lawmakers say GM’s ignition switch defect may have come to light sooner if the customers who settled with GM had not been compelled to sign confidentiality agreements.

U.S. Transportation Secretary Anthony Foxx has called for raising NHTSA’s maximum civil penalty from $35 million -- the amount of the record fine that GM was ordered to pay last month -- to $300 million.

None of these proposals have yet won the endorsement of key lawmakers such as Upton and Senate Commerce Chairman Jay Rockefeller, D-W.Va. Capitol Hill sources say the most likely route to passage is as an addendum to a broader package being written to rebuild the U.S. Department of Transportation’s dwindling highway trust fund.